I'm not a rocket scientist, but I would say the best way to cool the engine would be regenerative cooling, where the lox is pumped through a jacket around the engine.

If you haven't had a chance, I would suggest going to http://www.armadillaerospace.com and reading through their updates from about March 2005 on. The updates document the LOX/Ethanol engine development and all of the methods they have tried for engine cooling.

What is "best" depends of course on what your requirements are. Regenerative cooling requires more engineering than simpler methods, and you get the issue of having to deal with the coolant mass inside the tubes. But in terms of efficiency, impulse and lifetime, it's probably the best way.

Ablative cooling is simple, but it limits the lifetime of the engine.

Film cooling is also quite simple, and has potential for longer lifetime than ablative cooling.